Another sales job isn't what the holdouts want, of course — they want a credible plan that will actually result in defunding Obamacare — never mind that leadership doesn't think such a plan exists.

"I know I told them to go back to the drawing board," Rep. Lee Terry, R-Neb., said of the original leadership CR strategy.

When asked if he expected leaders would present a different game plan next week, Terry replied, "I would think, with so many of us mentioning to them that they need to come back with a different approach, there will be tweaks."

Speaker John A. Boehner, R-Ohio, and Majority Leader Eric Cantor, R-Va., are pushing for a CR to run through Dec. 15 at the 2013 sequester level. It would be sent to the Senate along with a sidecar resolution demanding the chamber take an up-or-down vote on defunding Obamacare before it can consider the stopgap spending bill.

Leadership aides said on Wednesday that the decision to delay consideration of the CR had nothing to do with a failure to garner the necessary threshold of votes, even on the rule to allow for floor debate.

“It’s complicated stuff and members have had very little time to process it,” a GOP leadership aide said on Wednesday. “Most people who think through all the moves in the legislative chess game realize this plan is likeliest to yield the best result — but it takes awhile to think and talk it through.”

In fact, everyone is reporting a different variation of a whip count, with Rep. Thomas Massie, R-Ky., saying there were between “50 and 80” holdouts and Rep. Marlin Stutzman, R-Ind., estimating that opponents added up to something closer to “a good dozen.”

But opponents of the current strategy — which they have called nothing more than a “gimmick” — are emboldened by the postponement and say they think it bodes well for a bolder plan to be unveiled next week.

Stutzman, while acknowledging that his whip count wouldn’t have threatened passage of the measure, still said he thought that leadership understood the reality that they had to come up with a better idea to appeal to lawmakers.

“I think just that discussion showed leadership ... that there was a problem with it and they’re going back to the drawing board to find another way to move forward because we want to move forward together as a conference and that idea wasn’t flying,” Stutzman said, adding that he very much expected to see “something different” next week.

Rep. Cynthia M. Lummis, R-Wyo., said she told the formal GOP whip team that she would vote “no” on the current proposal for a whole host of reasons — not just the handling of Obamacare defunding — and that she looks forward to seeing a new plan soon.

On learning from reporters that leaders have said they plan not to introduce a new proposal but to make a persuasive sales pitch for the current blueprint, Lummis said she was unaware of any such effort.

“That has not been explained to me,” she said. “I have not been invited to a small-group meeting. ... That’s news to me.”

There were other members on Wednesday who suggested they’d be willing to turn their “no” votes on the current CR proposal to a “yes” if they had the guarantee that leadership would pursue a strategy to delay or defund Obamacare in the next continuing resolution or, better, the bargain to raise the debt ceiling.

Rep. John Fleming, R-La., said on Tuesday that he was amenable to that scenario. Rep. David Schweikert, R-Ariz., added that he, too, was looking for “a well-articulated strategy where you could see the impact” on legislation to fund the government and dismantle the 2010 health care law.

“I wouldn’t say ‘no’ to any serious effort form the leadership to defund Obamacare, if they have a credible plan that has to happen in October or coincident with the debt limit or whatever,” Massie piped in. “I’ll listen to it.”

Punting to future battles on Obamacare has been the GOP leaders' go-to move since they took over in 2011. And there's no reason to think that leadership, which thinks shutting down the government Oct. 1 over Obamacare is a loser move, would give anything more than lip service to the idea of demanding Obamacare defunding to resolve a default crisis in mid-October or to keep the government open in December.

But the fact some holdouts are even floating the possibility of willingness to vote for the CR in return for future promises suggests some lawmakers are starting to look for an escape hatch.

Stutzman, for one, doesn't want to postpone the fight.

“It has to be done on the CR,” he said on Wednesday. “If it goes to the debt ceiling, I’m not willing to take those calculations."